For me, the phrase "taste and see" was kind of an ambiguous thing. Whatever it was, I guess my general connotation would be with "enjoy" and "delight" in what I know about God, to meditate upon God's attributes and His great work. Certainly a good practice apart from this verse.
But on Sunday, I had the blessing to be able to sit in on a Bible study where they went through Psalm 34. One of the questions posed was, "What exactly does it mean to 'taste and see'?" Unless you're Catholic (or Lutheran), it really isn't possible for us now to "taste and see" God in a physical manner. Through that Bible study, the phrase took on an entirely new light.
If we actually look at the context, we see that "taste and see" is probably best interpreted by, "Trust in the Lord and see that He is faithful!"
Why is that? As one of the members of the Bible study encouraged us, "when in doubt, read the passage!"
Psalm 34's context (v.0) is that David has changed his behavior before Abimelech (Maybe Abimelech is the same person as Achish in 1 Samuel 21? Not sure what is going on with the names).
David sings this psalm and begins with "I will bless the LORD at all times" (v.1) and proceeds to encourage all of Israel to join him (v.3). He testifies that the Lord has "answered [him] and delivered [him] from all [his] fears." (v. 4) He then testifies that, "This poor man cried, and the LORD heard him and saved him out of all his troubles."(v.6) The promise is given that, "the angel of the LORD encamps around those who fear him, and delivers them." (v.7)
With all of that setting the background, what does the encouragement to, "taste and see that the Lord is good!" mean?
I think it's a clear encouragement to trust the Lord. To follow in the footsteps of David, who cried out and the Lord delivered him. Much like the Lord challenged Israel in Malachi to, "put me to the test...if I will not open the windows of heaven for you and pour down for you a blessing until there is no more need," David encourages Israel to put the Lord to the test, trusting in Him for provision and refuge.
Don't be like the "young lions" in v.8 who (presumably) trust in their own power and might and suffer "want and hunger," but instead seek the Lord, relying on Him for deliverance and hope.
So to paraphrase, "trust and see that the Lord is good!"