That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved.
Note 9 at Ro 10:9: Remember that, in context, Paul had been contrasting two types of righteousness (see note 2 at Ro 10:3). The righteousness of the Law binds a person up in "doing," while the righteousness of faith just receives what Christ has already done (see note 5 at Ro 10:5).
This verse is stressing the simplicity of receiving righteousness by faith, as opposed to the bondage of trying to produce our own righteousness that is by the Law (Php 3:9). An attempt to amplify too much on the conditions of this verse would counter the point that Paul was making. However, in light of other scriptures, some explanation needs to be given.
This verse is not saying that anyone who just says the words, "Jesus is Lord," and believes that He rose from the dead is born again (see note 2 at Joh 3:3). As explained in note 1 at Mr 1:24, the Greek word "HOMOLOGEO," translated "confess" here, means more than just saying words. It literally means "to assent, i.e. covenant, acknowledge" (Strong's Concordance). By looking at Jesus' statement in Lu 6:46, a true confession of Jesus as Lord has to be heartfelt enough to involve a person's actions.
There are some groups that interpret the word "Lord" in a way that denies the deity of Jesus (see note 3 at Lu 1:43 and note 8 at Joh 5:23). This confession of Jesus as Lord has to be a declaration of faith in Jesus as God manifest in the flesh (1Ti 3:16). A Jesus who is less than God could not provide salvation for the whole human race.
Therefore, this verse is a promise to those who believe on Jesus to the extent that they are willing to change their actions accordingly and confess Him as Lord (God) with their mouths so that they might be saved.