Albert Barnes on 1 Thessalonians 4:1

Furthermore then. τολοιπον. "As to what remains." That is, all that remains is to offer these exhortations. 2Cor 12:11; Gall 6:17; Eph 6:10; Php 4:8. The phrase is a formula appropriate to the end of an argument or discourse.

We beseech you. Marg., request. The Greek is, "we ask you"-- ερωτωμεν. It is not as strong a word as that which follows.

And exhort you. Marg., beseech. This is the word which is commonly used to denote earnest exhortation. The use of these words here implies that Paul regarded the subject as of great importance. He might have commanded them--but kind exhortation usually accomplishes more than a command.

By the Lord Jesus. In his name, and by his authority.

That as ye have received of us. You were taught by us. Paul doubtless had given them repeated instructions as to their duty as Christians.

How ye ought to walk. How ye ought to live. Life is often represented as a journey, Rom 6:4, 8:1, 2Cor 5:7, Gall 6:16, Eph 4:1.

So ye would abound more and more. "That is, follow the directions they had received more and more fully." Abbott.

(*) "Furthermore" "Finally" (1) "beseech" "request" (2) "exhort" "beseech" (a) "walk" Col 1:10 (b) "abound" 1Cor 6:15,18