Question: "What is a carnal Christian?"
Answer: In answering your question about carnal Christians, lets first define the term "carnal." The word "carnal" is translated from the Greek word "sarkikos," which literally means "fleshly." This descriptive word is seen in the context of Christians in 1 Corinthians 3:1-3. As you read this passage, you see that the apostle Paul addresses the readers as "brethren" and then goes on to describe them as "carnal." Therefore, we can conclude that Christians can be carnal in their lifestyle. This may mean that a person does not have an active prayer life, they're not seeking the Bible as an authority for their life, they're not regularly worshipping God with other Christians, and/or they are involved in the sinful ways of the world (see 1 John 2:15-16).
Back in 1 Corinthians 3, we see the answer to another part of your question as to whether such a person is really saved. Since eternal security is a fact of Scripture, even the carnal Christian is still a Christian. The person cannot lose their salvation, because salvation is a gift of God that He won't take away (see John 10:28; Romans 8:37-39; 1 John 5:13). Even in 1 Corinthians 3:15, the carnal Christian is assured of salvation....."If anyone's work is burned, he will suffer loss; but he himself will be saved, yet so as through fire." The question often is not whether a person lost their salvation, but whether a person was truly saved in the first place.
For Christians who become carnal in their behavior, God lovingly chastens (disciplines) them as seen in Hebrews 12:5-11, so they can be restored to close fellowship with Him and be "trained" to obey Him. May the Lord bless you with assurance of your personal salvation and confidence in the eternal security found in Christ to the point of daily devoting your life and lifestyle to Him!