Crypto wallet software manages your private and public keys.
All coins or tokens are stored as data on the blockchain, and in order to manage, store and send these assets, one uses a crypto wallet appropriate for the job.
If you have never had a crypto wallet before, or if you want to make a fresh brand new wallet, the most important aspect of your wallet software is the set of 12 or 24 mnemonic seed words that the wallet software will randomly generate. This “seed phrase” is then converted to your private key. Whoever knows the seed words will know the private key, and will thus have full control to spend any assets that are linked to the public key/address. There are a number of resources regarding how to safekeep these seed words, ranging from pencil-and-paper, etching on steel, encrypted password managers, etc. Never, ever disclose your seed words or private key to anyone (e.g. enter into any website, software, etc.), unless you are 100% sure that software is the genuine, legitimate wallet software for which you are trying to re-initialize your wallet.
Some wallet apps are specific to certain blockchains (e.g. BTC only), or only for similar blockchains (e.g. Ethereum Virtual Machine chains only); while some are multi-coin wallets capable of managing multiple different types of chains within the same wallet.
Some crypto wallet software can also accommodate multiple private keys (essentially multiple separate “accounts” under one umbrella) and you can toggle between active wallets when desired.
In sum, wallet software itself is just a gateway to manage your private and public key. At its very core, your private key IS your wallet, and the crypto wallet software makes it easy to manage this private key and all relevant transactions/interactions with the blockchain. Even if you uninstall the wallet software, your coins are still safe on the blockchain. Keep in mind, however, that if you also lose the seed words, then there is no way to re-generate the original private key, and your coins are essentially lost/stuck forever in that inaccessible wallet; therefore, be sure to prioritize the safekeeping of your seed phrase at all times.