What is the ability to work under pressure?

This relates to how you respond when put under pressure. In a work context, pressure can be defined as;

The stress or urgency of matters requiring attention, the burden of physical or mental distress and the constraint of circumstances.

The ability to work under pressure involves dealing with constraints which are often outside of your control - these might be resource or time constraints, the difficulty of the task or having insufficient knowledge required to complete the task, or unforeseen changes or problems. Effective planning and time-management (to mitigate or allow for unexpected problems for example) can reduce the likelihood of some pressurised situations occurring, but will not eradicate them completely.

Why do employers value the ability to work under pressure?

Changes and unexpected events, problems or challenges can - and do - often occur, regardless of how well-planned or organised you are. The ability to respond effectively to pressure and stress is therefore extremely important in any line of work. How you respond will vary from person to person; some people thrive on it and perform better when under pressure, others may panic or become ineffective. It is important that you are aware of how you act in such situations and what steps you can take to improve your effectiveness in such situations if necessary.

Examples of how the ability to work under pressure can be developed or evidenced

Dealing with an emergency.
Overcoming problems or issues to achieve a goal, e.g. losing assignment data or work.
Reorganising responsibilities in a group task if one member unexpectedly drops out.
Managing well when work is unexpectedly busy or short staffed.

http://careerweb.leeds.ac.uk/info/4/make_yourself_employable/202/employability_skills/13
http://trendyslimdiggy..com/2014/08/what-is-ability-to-work-under-pressure.html

In a work environ,it is also defined as when ur wife calls to inform u dat her shop's about to be demolished by development control while ur caretaker is in ur office with a court order to throw out ur belongings unless u pay outstanding rent (which of course u dont ve) and ur office line rang to intimate u dat d youths of ur village re on rampage and ur aged father was innocently arrested by JTF as a boko suspect about to be "accidentally dischrged" if d youths dont chill, while ur supervisor just screamed at u to find out whats holding his report frm ur unit (made up of only u of course) which head office needs for a presentation to d MD 30mins ago (which of course 'll take u 1hr to prepare),and u happen to be a bank teller with a hall full of students to be paid bursary while network is down or slow.And as if d day is not already bad enough, ur bank's no 1 customer walks in & being in a hurry (in their usual manner) insists that u attend 2 him pronto, now dats working under pressure