Entry from OED Online

[Of obscure origin, but cf. POSH n.² The suggestion that this word is derived from the initials of ‘port outward, starboard home’, referring to the more expensive side for accommodation on ships formerly travelling between England and India, is often put forward but lacks foundation. The main objections to this derivation are listed by G. Chowdharay-Best in Mariner's Mirror (1971) Jan. 91-2.] 

    Smart, ‘swell’, ‘classy’; fine, splendid, stylish; first-rate. Also absol. as n.
  The pronunciation (p), a supposedly ‘posh’ or facetious way of saying the word, is occasionally heard. Quot. 1903 may exemplify a different word.
 
  [1903 WODEHOUSE Tales of St. Austin's 37 That waistcoat..being quite the most push thing of the sort in Cambridge.] 1918 Punch 25 Sept. 204 Oh, yes, Mater, we had a posh time of it down there. 1923 WODEHOUSE Inimitable Jeeves vii. 72 Practically every posh family in the country has called him in at one time or another. 1925 W. DEEPING Sorrell & Son ii. 22 Tips. Don't forget the tips. If a man's obliging—... It's a posh job. 1927 —— Doomsday xiv. 153 ‘You like it.’ ‘It's the poshest thing I've ever seen, old chap.’ 1927 —— Kitty xxix. 372, I say—that's a posh show. 1927 Daily Tel. 24 May 9 It was a club in Ham-yard—not a very posh club. 1929 J. B. PRIESTLEY Good Companions II. v. 391 I'd like to have..a very cosy car, small but frightfully posh. 1930 AUDEN Poems 63 To be posh, we gather, One should have no father. 1935 C. DAY LEWIS Time to Dance 32 For no silver posh Plane was their pigeon..But a craft of obsolete design. 1941 BAKER Dict. Austral. Slang 56 Posh, do the, to spend lavishly, do something ‘in style’. 1954 [see GROUND n. 11b]. 1957 J. OSBORNE Look back in Anger I. 13 Jimmy: Haven't you read the other posh paper yet? Cliff: Which? Jimmy: Well, there are only two posh papers on a Sunday. 1958 K. AMIS I like it Here viii. 98 This railway..though posher and faster, had often reminded him of the tram-like train. 1959 20th Cent. Nov. 377 At the time..none of the posh papers carried television reviews. 1970 [see CHEZ]. 1977 Lancashire Life Nov. 153/1 The poshest Granada Ghias..have electric windows. 1979 E. CAVE Blood Bond I. iii. 35 Charles's penchant for the grand—the ‘posh’ as Tom would have called it.
 

    Also pejoratively, (affecting to be) superior, upper-class, or genteel; ‘snooty’. (Earlier and further examples.)
 
  1915 Blackwood's Mag. CXCVIII. 255/2 Posh may be defined, very roughly, as a useless striving after gentlemanly culture. 1958 A. SILLITOE Saturday Night & Sunday Morning vii. 95, I suppose you're too stuck up now you've got such a posh job. 1979 London Rev. Bks. 25 Oct. 1/4 He gets a menial job at a posh private school. 1987 N. HINTON Buddy's Song xiii. 73 The people were obviously very rich and they talked in an extremely posh way.