You need to put the snippet into a folder with the name of the mode to use it in as follows:
 
`snippets/org-mode/diary_template`

Check out the documentation:

[Organizing snippets > Basic structure](http://joaotavora.github.io/yasnippet/snippet-organization.html#org91b0471):

```
.
|-- c-mode
|   `-- printf
|-- java-mode
|   `-- println
`-- text-mode
    |-- email
    `-- time
```

[Expanding snippets > ... > Eligible snippets ](http://joaotavora.github.io/yasnippet/snippet-expansion.html#orga555023):

> YASnippet does quite a bit of filtering to find out which snippets are eligible for expanding at the current cursor position.
>
> In particular, the following things matter:
>
> - Currently loaded snippets tables
>
>    These are loaded from a directory hierarchy in your file system. See Organizing Snippets. They are named after major modes like html-mode, ruby-mode, etc…
>
> - Major mode of the current buffer
>
>    If the currrent major mode matches one of the loaded snippet tables, then all that table's snippets are considered for expansion. Use M-x describe-variable RET major-mode RET to find out which major mode you are in currently.
>
> ...