t-extend is used to extend an existing template

You will see qweb templates in the base module like:

<t t-name="layout">
....
</t>

You can use <t t-extend="module_name.layout" > to extend these and insert new qweb elements.

<t t-jquery> is used to specify a postion.

For example,

<t t-name="layout">
<span class="some_class">Hello</span>
</t>

You could extend this by using:

<t t-jquery="span.some_class" t-operation="after">
</t>

t-jquery is usually used in conjuction with t-operation much like <xpath expr="" position="" /> 

Hope this helps.