Search - One or more property databases have fragmented indices.

Heavily fragmented indexes can degrade query and crawl performance.

Cause :

Fragmentation exists when indexes have pages in which the logical ordering, based on the key value, does not match the physical ordering inside the data file. All leaf pages of an index contain pointers to the next and the previous pages in the index. This forms a doubly linked list of all index/data pages. Ideally, the physical order of the pages in the data file should match the logical ordering. Overall disk throughput is significantly increased when the physical ordering matches the logical ordering of the data.
Effects on Performance :

1. Query latency might increase.
2. Crawl rate may decrease as more time is spent writing metadata to the property database.
3. The property database defragmentation health rule detects that one or more property databases have fragmented indexes and attempts to correct the fragmentation. Note: when this rule is correcting the fragmentation, query latency and crawl rate are affected.
If you see a message like "Search - One or more property databases have fragmented indices." in Central Administration > Monitoring > Review Problems and Solutions

One of the possible Resolution is :

1.Go to Central Administration > Manage service applications > Search Application > Index reset in Left navigation > Reset Now
2.Go to Central Administration > Manage service applications > Search Application > Manage Content Sources > Sart Full Crawls for Content sources in the order of importance as per you business needs.

Reference :    One or more Search property databases have fragmented indices (SharePoint Server 2010)