Some foods are best experienced by tasting them for yourself. No matter how well someone may explain, expound upon or describe them there is nothing like tasting for yourself. Humans are born with the ability to detect five types of taste- sweet, sour, salty, bitter, and umami- though our individual sensitivity to each is largely determined by genetics. However, the way we feel about a certain flavor is much more up for grabs and influenced by our background and environment. So some of us prefer more saltiness, while others desire more sweetness. Because for each of us it is a different experience.
And so it is with God. For each of us, we bring a unique set of experiences to our relationship with God. However, the Psalmist wants us to know that there are some common attributes about God that will play out in different ways in our lives and therefore we have to try Him for ourselves rather than rely on someone else's experience with God. How God works in your life may be very different in someone else's life!
So taste and see for yourself says the Psalmist because God is a refuge, who provides resources, and is always reliable.