It is a wavelet which is 0 outside some finite interval [a,b].

If the f-wavelet is a bounded function with a compact support, then the

corresponding m-wavelet is also bounded and has a compact support.

See pages 4-5 of

Article Uniform Convergence of Compactly Supported Wavelet Expansion...

This is a good question.

A good place to start in answer this question is

C.K. Chu, W. He, J. Stoeckler, Nonstationary tight wavelet frams, I: Bounded intervals, Applied Comput. Harmonic Analysis 17, 2004, 141-197:

http://ac.els-cdn.com/S1063520304000454/1-s2.0-S1063520304000454-main.pdf?_tid=7038a9a0-8ebb-11e4-9f98-00000aab0f6b&acdnat=1419789822_b4d065d858867bbf3b11f9a2e22efe0f

See page 193 for an example of compactly supported spline functions (normalized tight wavelet frame).    See, also,

A. Cohen, I. Daubechies, J.-C. Feauveau, Biorthogonal bases of compactly supported wavelets, Communications of Pure and Applied Math. XLV, 1992, 485-560:

http://www.math.duke.edu/~ingrid/publications/CPAM_1992_p485.pdf

and

A. Cohen, I. Debauchies, Orthonormal bases of compactly supported wavelets III, SIAM J. Math. Anal. 24, 1993, no. 2, 520-527:

http://www.math.duke.edu/~ingrid/publications/SIAM_J_Math_Anal_24_p520.pdf

A very nice introduction to compactly supported wavelets is given in

L.A.  Barford, R.S. Fazzio, D.R. Smith, An introduction to wavelets, 1992:

http://www.hpl.hp.com/techreports/92/HPL-92-124.pdf

See the attached image for a compactly supported Daubechies wavelet.

It is a wavelet which is 0 outside some finite interval [a,b].

If the f-wavelet is a bounded function with a compact support, then the

corresponding m-wavelet is also bounded and has a compact support.

See pages 4-5 of

Article Uniform Convergence of Compactly Supported Wavelet Expansion...

The closure of the set upon which the wavelet stands non vanishing is a compact set.. That is if  ψ  is a wavelet function, then  cl({x:ψ(x)≠0}) is a compact set,  to say ψ is a wavelet of compact support. 

FOR THOSE WHO ARE NOT COMFORTABLE WITH TOPOLOGY AND/OR FUNCTIONALANALYSIS LET US SIMPLY SAY THAT THE WAVELET IS ZERO OUTSIDE A N INTERVAL [a,b] (FINITE & CLOSED)...

It means that the wavelet has a finite non-zero length which will result in increasing the probability of capturing events in short time instances.

YRS THIS LAST ANSWER  IS  A VERY USEFUL REMARK ABD MAKES IT VERY PROBABLE VIA THE INVERSE WAVELET TRANSFORM TO BE ABLE TO RECONSTRUCT WITH MINIMAL ERROR THE INITIAL SIGNAL