The portfolio beta is simply the beta of a portfolio rather than a single security. It is most often used as a measure of how risky a portfolio is, and as such is used in performance measurement, for example in the Treynor index.
The portfolio beta may be calculated in the same way as the beta of a security by calculating the covariance of the portfolio with the market. This approach may be preferable when assessing the past risk (e.g. for risk-adjusting past performance) of a portfolio the composition of which has changed over the period of interest.
The beta of a portfolio as it is at a point in time is the weighted average of the betas of its constituents. The weighting is simply the proprtion of the portfolio in that security: so the beta of a portfolio that is invested 15% in a, 40% in b and 45% in c is simply 0.15 × βa + 0.4 × βb + 0.45 × βc. This is simpler if the composition of the portfolio has not changed over the period being looked at, or if the changes have not significantly changed the beta.