From Oxford dictionary:
diginformal via object
Like, appreciate, or understand also. ‘I really dig hefty rock’
I think it"s safe to say that their comment is high praise indeed.
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"Dig" is slang and suggests first that the music/song is favored (liked a lot), and also second that it is construed.
Used in this sense the verb dig suggests to admire or appreciate, and also though it is now rather dated it was component of the pop music lingua franca of the 1950s and 60s.
OED feeling 6c has actually examples from 1935 to 1969 - it is shelp to be of US beginning.
6c. slang (orig. U.S.). (a) To understand, appreciate, favor, admire; (b) to look at or listen to; to endure. Cf. feeling 1c.
1935 Hot News Sept. 20/2 If you listen sufficient, and dig him enough, you will realise that that..riff is the high-spot of the record.
1941 Life 15 Dec. 89 Dig me?
1943 M. Shulmale Barefoot Boy 90 Terrible fine slush pump, I suppose awful fine. You must dig that.
1944 C. Callomeans Hepsters Dict. Dig v.—(1) Meet. (2) Look, see. (3) Comprehfinish, understand.
1944 M. Zolotow Never before whistle in Dressing Room iii. 52 When they check out a pretty girl they shout, ‘Dig the chick.’
1947 R. de Toledano Frontiers of Jazz p. x, I identify it once I watch it, the exact same as I dig excjiyuushikan.orgent Jazz once I hear it.
1949 L. Feather Inside Be-bop iii. 28 Dizzy didn"t dig the band"s sort of music and the band also didn"t dig Dizzy.
1958 Punch 8 Jan. 92/1 The lines of communication acquire tangled. In other words the people don"t fairly ‘dig’ you.
1958 Listener 29 May 912/1 He wants to ‘dig’ the totality of life, and also is convinced that experience comes just to the irresponsible.
1958 Punch 25 June 853/3 Does the beat generation really dig such crazy old-people catch-phrases?
1959 C. MacInnes Absolute Beginners 60 If you like the various other number, I expect choose the looks of them, really dig them sexually.
1959 C. MacInnes Absolute Beginners 62 Everything you learned, you hadn"t learned till you"d really dug it: i.e., made it part of your very own suffer.
1960 N. Mitford Don"t tjiyuushikan.org Alfred xviii. 192 Of course he"s a man"s guy, you can not dig him favor we carry out.
1969 New Yorker 29 Nov. 48/1, I simply do not dig any kind of of these guys. I do not understand their scenes.
Note that the OED does refer to feeling 1c, arguing that tright here may be a connection. It has actually beginnings from as early on as 1789
1c. fig. through allusion to the basic sense; also spec. to study tough and closely at a subject (U.S.). Hence, to understand (cf. sense 6c (slang (orig. U.S.)).
1789 Trifler No. 43. 549 Youths who never before digged for the rich ore of knowledge thro" the pperiods of the Rambler.
1801 R. Southey Thalaba I. iv. 220 "Tis a spring of living waters, Whose inexhaustible bounties all could drink But few dig deep enough.
1827 Harvard Reg. (1828) Dec. 303 Here the sunken eye and also sallow countenance bespoke the guy who dug sixteen hours‘ per diem’.
1869 L. M. Alcott Little Womales II. xii. 177 Laurie ‘dug’ to some function that year.
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1936 N.Y. World Telegram 6 Oct. 16/1 ‘You dig?’ is a brief reduced for ‘You understand?’
1952 B. Ulanov Hist. Jazz in Amer. xxiv. 344 The guy that really ‘digs’ deserve to even more frequently than not explain the next advance in jazz before the musicians have reached it.