Why there is a large lost+found folder on external disk I brought my MacBook Pro 1 year ago, at that time it runs OS X 10.9 . At that time I connected an external 2TB HDD (HFS+ single partition, not connected all the time) to it via USB as a Time Machine backup destination. Later I turned off Time Machine and use the HDD to store some pictures. Months after that I upgraded to OS X 10.10 and now 10.11 Beta 1. 

Today I noticed my disk space not enough so I scanned the disk for big files, only to find there is a lost+found folder in my external HDD, which takes nearly 1TB of space. The content of which is files I deleted during the days, most of them originated from internal SSD (And I never put them into that HDD), the create time of which are all in 2014. All the files are named like iNodexxxxxxxxxx and directories dir_xxxxxxxxxxx .

Why are my deleted files now found in an external disk? Is it safe to delete the whole folder without affecting anything outside?
The name is historic from unix. The filesystem is designed to track files and when there is a problem, the filesystem will under some repair operations, lose files to remain workable. (hence the need for backups)

Those files that would be lost in this operation are stored in the lost+found folder so that you could perhaps use them if they are undamaged or at least inspect them to know what files are now corrupt or missing.

The program that moves files into lost+found and repairs the filesystem is [fsck][1]

You should delete the folder and all it's contents once you decide you don't need to learn anything from it. Also, you should run Disk Utility or fsck to see if you can get a clean run or if you need to erase that volume and start over/replace it.