An “out-of-pocket” expense or cost is something that someone has to pay himself or herself. For example, on a business trip, there could be out-of-pocket expenses such as gas and meals. Sometimes out-of-pocket expenses are reimbursed by an employer and sometimes out-of-pocket expenses are tax deductible.
 
“Out of pocket expenses” has been cited in print since at least 1828 and “out-of-pocket costs” since 1831.
 
   
Wikipedia: Out-of-pocket expenses
Out-of-pocket expenses are direct outlays of cash which may or may not be later reimbursed.
 
In operating a vehicle, gasoline, parking fees and tolls are considered out-of-pocket expenses for the trip. Insurance, oil changes, and interest are not, because the outlay of cash covers expenses accrued over a longer period of time.
 
The services rendered and other in-kind expenses are not considered out-of-pocket expenses, nor are depreciation of capital goods or depletion.
 
Answers.com
Barron’s Business Dictionary: Out-Of-Pocket Expenses
Expenditures out of a taxpayer’s own funds for business or personal use. For example, unreimbursed out-of-pocket expenditures for telephone, uniforms, or equipment incurred in rendering services to a charitable organization may be deductible as a charitable contribution.
 
Investopedia
Definition of ‘Out-Of-Pocket Expenses’
An expense incurred and paid for by an individual for personal use, or relating to one’s employment or business. This can also relate to ongoing costs of operating a fixed asset, such as a car or a home. 

Some out-of-pocket expenses may be reimbursed by an employer or other group if the expense is incurred directly on their behalf.
 
The Free Dictionary
out-of-pocket expenses
Fig. the actual amount of money spent. (Alludes to the money one person pays while doing something on someone else’s behalf. One is usually paid back this money.)
 
Merriam-Webster Dictionary
out–of–pock·et adj \-ˈpä-kət\
Definition of OUT-OF-POCKET
: requiring an outlay of cash “out–of–pocket expenses”
First Known Use of OUT-OF-POCKET
1885
 
(Oxford English Dictionary)
out-of-pocket adj. and n.
1885 Law Times Rep. 52 545/1   The plaintiffs..incurred various out-of-pocket expenses.
1973 ‘I. Drummond’ Jaws of Watchdog vii. 92   He was to be paid £15,000 in used notes, for his own pay-off and his out-of-pocket.
1994 Amer. Scientist Oct. 451/3   Let us ignore the out-of-pocket costs of travel.
     
Google Books
History of George Godrey
Written by Himself
London: Henry Colburn
1828
Pg. 33 (Volume II):
The juries will give only a farthing damages, of course; but then the costs — the costs, you know; so we get them, we shall do: and these (out of pocket expenses deducted), we will divide between us.”
 
Google Books
Six letters on subjects very important to England
By Sir George Cockburn
London: WIlliam Blackwood
1831
Pg. 164:
... and if the taxed costs, on the whole, and the out-of-pocket costs on same, by both parties, were calculated, it would be found, that to recover the L.50 it cost L.150.
 
Google Books
15 August 1840, The Legal Observer, pg. 298, col. 2:
Here, what expenses (out-of-pocket expenses too) were incurred, for no one useful purpose?
 
12 July 1854, The Nonconformist (London), pg. 574, col. 3:
He (Mr. Gidley) had stated to the registrar, that it was his wish not to put the man to any unnecessary expense; the out-of-pocket expenses must, of course, be paid, but his own charges would be nominal.
 
Chronicling America
6 March 1892, Pittsburg (PA) Dispatch, “Princely Perquisites,” pg. 7, col. 2:
LONDON, March 5.
(...)
... and actually urge than an ambassador or minister should send in his bill like any common person and receive only out-of-pocket expenses.