It is the actual physical body and blood of Jesus Christ to us.
Since I am a Southern Baptist, I am to adhere to the Baptist Faith and Message, which says on this subject:
"The Lord's Supper is a symbolic act of obedience whereby members of the church, through partaking of the bread and the fruit of the vine, memorialize the death of the Redeemer and anticipate His second coming."
I think our interpretation has much to do with Luke 22:19-20:
19 And he took bread, gave thanks and broke it, and gave it to them, saying, "This is my body given for you; do this in remembrance of me." 20 In the same way, after the supper he took the cup, saying, "This cup is the new covenant in my blood, which is poured out for you."
In fact, on the face of our own church's altar, before which the Supper is administered, it is literally chiseled "Do This In Remembrance Of Me". I understand "our" argument that Jesus was instituting a fundamental and extremely important remembrance through symbolism. The Bible is replete with symbols and reminders for us. He knows how dumb we are, and He's right! :) I suppose I just don't understand the "level" of literalness that Catholics believe, since no credible person argues that the disciples actually ate of His flesh and drank of His blood. The passage does not support that at all anyway, they were breaking bread.
This is not intended as a "we are better than you are" measure. Rather it is intended to ensure that those taking the sacrament do not do so unworthily and thereby bring judgment upon themselves. Scripture expressly warns that taking the body and blood unworthily can be to your judgment.
We also urge caution to the extent that nonbelievers should not take the Lord's Supper in our church. I don't know those verses, but I would imagine that our respective churches would quote similar scripture. I wonder if there is a difference for a hypocrite vs. an unknowing violator.
Just to bring in another view, I Corinthians 11 is the passage that talks about taking communion "unworthily." A better translation is an unworthy manner. The manner which is being specifically spoken of in this passage is that certain people are being excluded from partaking because they are poor and working late, and the rich are getting drunk. As a result there's none left by the time the poor get there. It's interesting to me that Jesus seemingly made no effort to exclude Judas from the communion table.
I think the clear warning for the church is to not use communion as a way of defining who's in and out. Certainly there is room for church discipline and confronting sin, but using communion to do so brings judgment upon the leaders who do it.
Instead, the reason Catholics do not extend Communion to non-Catholics is the existence of historic schism. We are in schism vis-a-vis the Protestants and, sadly, the Orthodox (and the latter say the same thing to us; Protestants used to say it but their view of the Church isn now so confused that they no longer say it or if they do, it's lost most of its meaning--the denominational theory says that all denominations are partially right and partially wrong). Until the schism is healed, exchanging the sign of unity (Communion) would be a lie and lies are always bad.
Other forms of fellowship with fellow Christians (= the baptized) are possible, just not this one because it, more than any other sign, signifies unity, unity that does not now exist.
Those Protestants who devalue historical unity/disunity and place their hope in "spiritual unity" see no reason not to share the Eucharist among all who are baptized. So it comes down to the question of how important historic unity and schism are.