A battle-barge is a large capital ship employed by Space Marine fleets. With the exception of the mobile fortress-monasteries employed by some Chapters, they are the largest capital ships available to the Space Marines. A Chapter will generally have two or three, though some have more (e.g. the Ultramarines have five and the Space Wolves have EIGHT).
The term itself is more of a ship type than a specific pattern; the Adeptus Mechanicus does produce a special pattern of ship just for Space Marines, but any ship can be used as a battle barge so long as it has enough capacity to launch vast quantities of Thunderhawks and Drop Pods and enough weapons and armor to protect them. A standard battle-barge has the facilities for three entire companies to operate out of, including support staff and logistics, such as vehicle repair.
No matter what they start as, or what they look like, battle-barges (like all Space Marine starships) are specialized for planetary assault. They have relatively little long-range firepower, but instead have enough hangar and torpedo bay capacity to launch three full companies of Space Marines at once, perform an orbital bombardment, or even commit Exterminatus.
How something as ridiculously huge as a battle-barge can only provide facilities for two to three hundred Space Marines when a modern amphibious assault ship which is literally thousands of times smaller in terms of volume can fit nearly ten times that number of people as well as landing craft, VTOL support, and vehicular support is anyone's guess. It seems that a lot of fluff writers themselves consider this kind of dumb given how often more than three hundred marines get stuffed onto one Battle-Barge.
To put this into perspective, at only three hundred Space Marines per battle-barge, a single battle barge could provide every Space Marine inside their very own fucking hundred bedroom royal palace complex with nearly every luxury known to man provided inside and still have enormous amounts of space left over. It would be essentially impossible for the Space Marines to defend the battle barge against boarders because there'd be so much empty space that any invader could just go around. You could literally have a thousand times more Marines in one battle barge and it'd still be considered to be pretty roomy inside.
Any explanations for this absurdly low number - be they official lore or inferred by the fans - vary widely, and one could easy dismiss it as GW's sense of scale being severely miscalibrated (as usual), but there are justifications for it that hold together under scrutiny. Astartes vessels are supposed to be amongst the fastest and most technologically advanced vessels the AdMech can make, so perhaps battle barges are designed and/or modified to give them the best possible thrust-to-weight ratio possible by eliminating every unnecessary tonne and empty space, with anything that doesn't absolutely require human involvement using the arcane and mysterious practice of...automation!
That said, the the best explanation is actually one of logistics; after the Horus Heresy and implementation of the Codex Astartes, the vast majority of Space Marine chapters consist of one thousand battle-brothers divided into ten companies of one hundred marines each, and since it's basically unheard of for any given chapter to not have battle-brothers fighting in the Imperium's ceaseless wars at any given time, the actual number of marines in their roster is usually lower due to casualties taken in battle. Furthermore, the time it takes to replenish the chapter's numbers means that they can't afford to lose large numbers of Marines on a regular basis. All of this adds up to the entirely reasonable precaution that three hundred marines is the generally accepted maximum number to be on board a single battle barge at any given time. If that barge gets destroyed with all hands it's an unmitigated disaster, and putting the entire chapter on a single vessel is basically flirting with suicide.
Notable Battle Barges
Daughter of Tempests: A Lamenters Battle Barge deployed during the Corinth Crusade, in support of the Ultramarines.
While crusading the glorious motha-fukas of the most put upon Chapter in Imperial history learned of an Ork slave world cheerily named Slaughterhouse III. When the Lamenters were told that no other forces could be spared to free the world from the greenskin menace, they took it upon themselves to do so. When Daughter of Tempests jumped to the system, she intentionally emerged from the warp absurdly close to the Orkish defenses of the planet; the greenskins were taken by surprise and didn't get a shot off before the Daighter had disabled the orbital guns and deployed 300 yellow armored Sons of Sanguinious to the surface. She then assisted in the evacuation of 3 million survivors before the Lamenters declared Exterminatus to deny the Orks access to the planet's resources.
She was destroyed during the Badab War when the Minotaurs ambushed the Lamenters Chapter Fleet and forcibly boarded their ships.
Vulkan's Wrath A Ship from the Salamanders that took part in the Commorragh Raid.
When "Those Knife Eared Assholes" swiped the Salamander Strike Cruiser Forgehammer from Real Space and stashed it in their City, Vulkans Wrath lead a fleet Of Salamanders, Howling Griffons, and Silver Skulls into Commorragh itself to rescue their brothers. With the forces of 3 Chapters of Space Marines wreaking havoc in the streets, the missing cruiser was located, held down by an Electric Spire. Terminators deployed from Vulkan's Wrath teleported to Forgehammer's decks and loosed the cruisers missile battery on the spire. With Forgehammer free, Vulkan's Wrath lead the strike group out of the Dark City and into the safety of Imperial space.
Tempestus: The Flag Ship of the Astral Knights.
Tempestus was the battering ram on which the Astral Knights rode to their Glorious Destiny in the battles against the World Engine.
After the destruction of the World Engine and the entire chapter, Tempestus was salvaged and converted into an Imperial Shrine dedicated to the 772 Heroes of the Astral Knights on the world of Safehold, the last planet scoured by the World Engine.
Macragge's Honour: Flagship of the Ultramarines.
Don't let that fool you. This ship is badass, as in destroying-a-traitor-battle-barge-in-the-warp badass. After it was overrun by demons twice and heavily damaged. It took out the Word Bearers' Battle Barge Infidus Imperator during the Battle of Calth, to clarify. One of the last of the colossal Gloriana Class Warships still in existence, it is over twice as long as an Emperor class Battleship and even rivals a Super Star Destroyer in length or significantly exceeds it depending on what measurements you use. Given the rather "deep" construction of most ships in 40k, the Macragge's Honour would almost definitely exceed the Executor in terms of volume even with more low end measurements anyway given how flat the latter is. It is currently the Lord Commander's flagship again and can be thought of as the de facto flagship of the Imperium as a whole, or at least a contender for that title with the Phalanx being the other one.
Given that even the entirety of the Ultramarines combined would not be able to adequately crew the Macragge's Honour, it probably has crew complements from multiple chapters of Guilliman's successors to crew it up to Heresy era standards.