How does a contactor work &its no nc functions

A contactor/relay usually uses a lower voltage to energize contacts for Larger Current and or Voltage. Many AC Compressors use a Doublepole/Single Throw Contactor with a 24 Volt coil.
If is is Double Pole Single Throw, you have a common, a NO(Normally Open Contact to Common) and a NC(Normally Closed Contact to Common).
When the coil has voltage the NC contacts open, and the NO contacts, close.

I have to clarify Strat's post because it's not entirely correct.

NO - Means Normally Open when depenergised
NC - Means Normally Closed when de-enerzised

Contacts have Form numbers associated with them e.g. Form A, Form C etc. Won't go into details.

Common relays may have a Common, NO and NC contacts. This acts like an SPDT type switch.

A contactor generally only cares about the open state. So there are two terminals. NO & C for the sake of argument. Usually pin #'s are assigned.

There is another type of switch and/or contactor that instead of having a common, it has two normally open contacts and say two normally closed contacts. There is no common connection.

The Fan Center in a furnace may be of the variety of two NO contacts and two NC contacts without a common connection. This is typically used when the system has to change the speed of a motor. One set of contacts will have to completely disingauge before the other set of contacts will engage.

In industry, it's common to have to purchase contact blocks for industrial switches. They are typically of the NO and NC variety without a common terminal.

Kiss, I don't see my mistake.

It's not that you were wrong.

But, it does not include the case depicted on figure 9 here http://customer.honeywell.com/techli...0s/60-2023.pdf

It doesn't include these http://www.alliedelec.com/Images/Pro...OL_8140201.PDF
Type of contact blocks:

1NO-1NC can be configured as an SPDT switch, but it isn't.