You, as an adult in a society, have presumably been able to make yourself understood (including to yourself) for a long time, so "we understand what each-other are saying and can imagine one another's feelings" is a basic subtext of essentially every conversation you have.

Toddlers, on the other hand, are still working on gaining enough linguistic capability to make themselves understood and understand what others are saying, and are still gaining self-awareness of their feelings, needs, and the way the world around them works. Remember that within very recent memory they could only make their needs known by screaming. Validating their emotions and needs confirms that you actually, mechanically understand what they want, and in some cases helps them recognize in fact what they want, both of which can undermine the frustration at the root of the tantrum.