For a good quick look at the difference between aramaic and hebrew, see
here. The Gemara, an important section of the Talmud, was written in Aramaic, by the rabbis. It is clear that the common people only understood Aramaic, not Hebrew because of the use of targums, that is, Aramaic paraphrases of the Torah, usually read after the Hebrew reading of the Torah. Some of the Dead Sea Scrolls are targums, which date to the first century.
However, the strongest evidence is in the New Testament itself. Here is an exhaustive list of Aramaic words in the NT. Note that most of them are names, but it still is interesting that some phrases were left untranslated into Greek.
There are many Aramaic words preserved in the Greek of the N.T., and most of the commentators call attention to a few of them; but, from the books cited below, we are able to present a more or less complete list of the examples to which attention is called in the notes of The Companion Bible (*2).
1. Abba (*3). Mark 14:36. Rom. 8:15. Gal. 4:6.
2. Ainias. Acts 9:33, 34.
3. Akeldama. Acts 1:19. Akeldamach (LA). Acheldamach (T Tr.). Hacheldamach (WH). See Ap. 161. I. Aram. Hakal dema', or Hakal demah.
4. Alphaios. Matt. 10:3. Mark 2:14; 3:18. Luke 6:15. Acts 1:13.
5. Annas. Luke 3:2. John 18:13, 24. Acts 4:6.
6. Bar-abbas. Matt. 27:16, 17, 20, 21, 26. Mark 15:7, 11, 15. Luke 23:18. John 18:40, 40.
7. Bartholomaios. Matt. 10:3. Mark 3:18. Luke 6:14. Acts 1:13.
8. Bar-iesous. Acts 13:6.
9. Bar-iona. Matt. 16:17. See No. 27, below.
10. Bar-nabas. Acts 4:36, &c. 1Cor. 9:6. Gal. 2:1, 9, 13. Col. 4:10.
11. Bar-sabas. Acts 1:23; 15:22 (Barsabbas all the texts).
12. Bar-timaios. Mark 10:46.
13. Beel-zeboul. Matt. 10:25; 12:24, 27. Mark 3:22. Luke 11:15, 18, 19.
14. Bethesda. John 5:2. (Bethzatha, T WH; Bethsaida, or Bethzather, L EH Rm.)
15. Bethsaida. Matt. 11:21. Mark 6:45; 8:22. Luke 9:10; 10:13. John 1:44; 12:21.
16. Bethphage. Matt. 21:1. Mark 11:1. Luke 19:29.
17. Boanerges. Mark 3:17. (Boanerges, L T Tr. A WH.)
18. Gethsemanei. Matt. 26:36. Mark 14:32.
19. Golgotha. Matt. 27:33. Mark 15:22. John 19:17.
20. Eloi. Mark 15:34.
21. Ephphatha. Mark 7:34.
22. Zakchaios. Luke 19:2, 5, 8.
23. Zebedaios. Matt. 4:21, 21; 10:2; 20:20; 26:37; 27:56. Mark 1:19, 10; 3:17; 10:35. Luke 5:10. John 21:2.
24. Eli. Matt. 27:46. (Elei (voc.), T WH m.; Eloi WH.)
25. Thaddaios. Matt. 10:3. Mark 3:18.
26. Thomas. Matt. 10:3. Mark 3:18. Luke 6:15. John 11:16; 14:5; 20:24, 26, 27, 28, 29; 21:2. Acts 1:13.
27. Ioannes. John 1:42; 21:15, 16, 17. (Ioanes, Tr. WH.) See Bar-iona. (Iona being a contraction of Ioana.)
28. Kephas. John 1:42. 1Cor. 1:12; 3:22; 9:5; 15:5. Gal. 2:9.
29. Kleopas. Luke 24:18.
30. Klopas. John 19:25.
31. Lama. Matt. 27:46. Mark 15:34. (Lema, L. Lema, T Tr. A WH).
32. Mammonas. Matt. 6:24. Luke 16:9, 11, 13. (Mamonas, L T Tr. A WH.)
33. Maran-atha. 1Cor. 16:22 ( = Our Lord, come!). Aram. Marana' tha'.
34. Martha. Luke 10:38, 40, 41. John 11:1, &c.
35. Mattaios. Matt. 9:9; 10:3. Mark 3:18. Luke 6:15. Acts 1:13, 26. (All the critics spell it Maththaios.)
36. Nazareth (-et). Matt. 2:23; 4:13 (Nazara, T Tr. A WH); 21:11. Mark 1:9. Luke 1:26; 2:4, 39, 51; 4:16 (Nazara. Omit the Art. L T Tr. A WH and R.) John 1:45, 46. Acs 10:38.
37. Pascha. Matt. 26:2, 17, 18, 19. Mark 14:1, 12, 12, 14, 16. Luke 2:41; 22:1, 7, 8, 11, 13, 15. John 2:13, 23; 6:4; 11:55, 55; 12:1; 13:1; 18:28, 39; 19:14. Acts 12:4. 1Cor. 5:7. Heb. 11:28. The Hebrew is pesak.
38. Rabboni, Rabbouni (Rabbonei, WH). Mark 10:51. John 20:16.
39. Raka. Matt. 5:22. (Reyka' is an abbreviation of Reykan.)
40. Sabachthani. Matt. 27:46. Mark 15:34. (Sabachthanei, T Tr. WH.)
41. Sabbata (Aram. sabbata'). Heb. shabbath. Matt. 12:1, 5, 10, 11, 12, &c.
42. Tabitha. Acts 9:36, 40.
43. Talitha kumi. Mark 5:41. (In galilaean Aramaic it was talitha' kumi.)
44. Hosanna (in Aram. = Save us; in Heb. = Help us). Matt. 21:9, 9, 15. Mark 11:9, 10. John 12:13.
source:
http://www.angelfire.com/nv/TheOliveBranch/append94.htmlIndeed, a plausible theory is that the earliest versions of Matthew was written in Aramaic, not greek. This is based on word-play, semitisms, poetry, etc. See
http://www.aramaicnt.org/NEW/index.php? for a bit of an extreme take.