This paper tackles the problem of distributed sensing from a goal-oriented communications perspective. The case of sensors sampling sources in the environment and conveying the collected information to a fusion center over a wireless channel is considered. Herein, the objective of the communications is to achieve a reliable estimation of the sources, while preserving network resources. The fusion center task is formulated as a joint distributed sensing problem, where a scheduling policy has to be designed to optimize the applicative goal. Two distinct goals are considered: a) when the objective is to achieve the best possible estimation of the sources given a communication resource constraint; b) when the objective is to minimize the communication resource to estimate the sources up to a pre-determined precision. For both cases, the optimal scheduling policy is formulated as the solution to a constrained optimization problem. Greedy iterative algorithms are proposed to efficiently solve those problems for the particular case of independent sources. Numerical results illustrate the tradeoff between achievable estimation accuracy and resource consumption, and provide insights on the impact of the network structure on the achievable performance.