Daedalus wallet is one of several Daedalus wallet editions that is used on the Cardano blockchain. It is a software application for use on computers, there is no mobile version. Daedalus is the original wallet released for the launch of the Cardano blockchain in 2017.
Daedalus wallet is used on the Byron era Mainnet. During test cycles, prior to a new version release, it is also used on the Byron era Testnet (there are several testnets, see Cardano Networks for more details) for beta testing.
Daedalus is only available for download at https://daedaluswallet.io/#download
Pros & Cons
Online wallets are convenient since they give immediate access to your ada, however, like all software they are susceptible to risks like hacking and malware. On the other hand, paper wallets are less convenient but generally regarded as safer in terms of losing your ada.
See also Tips for Staying Safe Online
Daedalus is a full node wallet, developed by IOHK, which will allow you to store ada, the native cryptocurrency of the Cardano blockchain.
Daedalus is a Hierarchical Deterministic (HD) wallet, allowing you to create an infinite set of keys from a single seed (We call the seed the 12-word Daedalus wallet recovery phrase).
Whenever you want to move your Daedalus wallet or open it on a different device, you will only need to enter your 12-word Daedalus wallet recovery phrase and the HD algorithm will find all your ada. This means you will never have to worry about managing lots of 12-word Daedalus wallet recovery phrases or files for keys.
More information can be found at https://www.cardano.org/en/the-daedalus-wallet/