As you said there are three enzymes, known generically as E1, E2 and E3, which act in series to catalyze ubiquitination which is a multi-step process.
In humans there are two E1 ubiquitin activating enzymes responsible for activating ubiquitin, the first step in ubiquitination. It hydrolyses ATP and adenylates the C-terminal glycine residue of ubiquitin, and then links this residue to the active site cysteine of E1, yielding a ubiquitin-thioester and free AMP.
E2 is the ubiquitin-conjugating enzyme, to which the transfer of Ubiquitin from E1 to active site of cysteine of E2 via trans-esterification takes place.
E3 is the ubiquitin ligase, which selectively recognizes the target protein and transfers Ubiquitin from E2 to lysine residue of the target protein.
Repeated ubiquitination leads to poly ubiquitination of target protein. This target protein is accepted by proteasome for degradation and recycle.
E3 ligases also play a role in cell cycle control, mediating the degradation of cyclins, as well as cyclin dependent kinase inhibitor proteins. Therefore,
E3 ubiquitin ligases regulate homeostasis, cell cycle, and DNA repair pathways, and are also involved in a variety of cancers.
Apart from proteasomal degradation, ubiquitination plays important roles in transcriptional regulation, protein trafficking, including endocytosis and lysosomal targeting, and activation of kinases involved in signaling processes.