Uke grabs one of tori's wrists with one hand.
It is in uke's interest to maintain a good - full-palm - grip while keeping arms and shoulders mobile ("sticky grip"). At the same time, a vigilant connection is established via this grip.
Katate-dori is not the goal of the attack, but only the first contact. It enables uke to fix tori for a short moment or to move them into a position where uke can continue the attack.
Gyaku-hanmi katate-dori: When only katate-dori is announced, the execution from gyaku-hanmi (mirror position) is expected. This is one of the most common attacks in Aikido.
Ai-hanmi katate-dori: This execution in handshake position is always explicitly announced. Ai-hanmi katate-dori in osae-waza can be considered as a reaction by uke to prevent tori from drawing the sword. The execution of many techniques from ai-hanmi katate-dori has similarities with shomen-uchi.
Search "Basic Forms" page for videos showing KATATE-DORI
Terms used:
Ai-Hanmi, Gyaku-Hanmi, Shomen-Uchi, Uke, Tori, Osae-Waza, Aikido