Bitcoin is a community-run technology. The main idea behind Bitcoin is that the rules of the game are coded into the Bitcoin Core C++ language source code. Therefore, there is no single document that specifies what Bitcoin is or isn't. Or, put another way, the source code itself is the document.
So how do features get added or removed from the Bitcoin Core source code? That is where BIPs come in!
As this section's title suggests, BIPs are proposals sent by the community in order to improve Bitcoin technology. The idea is borrowed from the Internet itself, which uses RFC's to discuss possible improvements to the collection of protocols that make up the Internet. RFC's are "requests for comments" which are submitted by researchers and academics in order to try and improve the network.
BIPs are Bitcoin's version of RFC's. Coders, researchers, cypherpunks and Bitcoin enthusiasts may submit BIPs. In case the community accepts the suggestion, the idea behind the BIP gets committed into the main Bitcoin source code tree.
In short, BIPs are the process through which Bitcoin evolves. BIP 141 is a particularly famous proposal from 2015, because it specified SegWit for Bitcoin, which Coinbase has just adopted into their own transaction processing system.
See also: Here you can browse the full list of BIPs, starting with BIP #1 which specifies how future BIPs will be processed!