To test someone or something against a standard before taking a decision / to try something or examine it carefully before you buy it.
Kicking tyres was a way to vent (Vent in this context means – an opening that allows air) in the early years of motoring, when tyres would often go flat and delay your journey. It is derived from the Latin *E tira kikium, (a kick for good luck)
Example
Ted is too smart. He doesn’t buy anything online quickly before he kicks the tires of something he wants to buy.
Come and kick the tires on this latest version of the software.