org-element: Improve some docstrings

* lisp/org-element.el (org-element-parse-buffer, org-element-map,
  org-element-at-point, org-element-context): Be more verbose in
  docstrings.  Also fix typos.

lisp/org-element.el

@@ -3611,7 +3611,32 @@ recursion.  It can be set to the following symbols:
 When VISIBLE-ONLY is non-nil, don't parse contents of hidden
 elements.
 
-Assume buffer is in Org mode."
+An element or an objects is represented as a list with the
+pattern (TYPE PROPERTIES CONTENTS), where :
+
+  TYPE is a symbol describing the element or object.  See
+  `org-element-all-elements' and `org-element-all-objects' for an
+  exhaustive list of such symbols.  One can retrieve it with
+  `org-element-type' function.
+
+  PROPERTIES is the list of attributes attached to the element or
+  object, as a plist.  Although most of them are specific to the
+  element or object type, all types share `:begin', `:end',
+  `:post-blank' and `:parent' properties, which respectively
+  refer to buffer position where the element or object starts,
+  ends, the number of white spaces or blank lines after it, and
+  the element or object containing it.  Properties values can be
+  obtained by using `org-element-property' function.
+
+  CONTENTS is a list of elements, objects or raw strings
+  contained in the current element or object, when applicable.
+  One can access them with `org-element-contents' function.
+
+The Org buffer has `org-data' as type and nil as properties.
+`org-element-map' function can be used to find specific elements
+or objects within the parse tree.
+
+This function assumes that current major mode is `org-mode'."
   (save-excursion
     (goto-char (point-min))
     (org-skip-whitespace)
@@ -3640,11 +3665,12 @@ containing the secondary string.  It is used to set correctly
 (defun org-element-map (data types fun &optional info first-match no-recursion)
   "Map a function on selected elements or objects.
 
-DATA is the parsed tree, as returned by, i.e,
+DATA is an Org buffer parse tree, as returned by, i.e,
 `org-element-parse-buffer'.  TYPES is a symbol or list of symbols
-of elements or objects types.  FUN is the function called on the
-matching element or object.  It must accept one arguments: the
-element or object itself.
+of elements or objects types (see `org-element-all-elements' and
+`org-element-all-objects' for a complete list of types).  FUN is
+the function called on the matching element or object.  It has to
+accept one argument: the element or object itself.
 
 When optional argument INFO is non-nil, it should be a plist
 holding export options.  In that case, parts of the parse tree
@@ -3658,7 +3684,37 @@ representing elements or objects types.  `org-element-map' won't
 enter any recursive element or object whose type belongs to that
 list.  Though, FUN can still be applied on them.
 
-Nil values returned from FUN do not appear in the results."
+Nil values returned from FUN do not appear in the results.
+
+
+Examples:
+--------
+
+Assuming TREE is a variable containing an Org buffer parse tree,
+the following example will return a flat list of all `src-block'
+and `example-block' elements in it:
+
+  \(org-element-map tree '(example-block src-block) 'identity)
+
+The following snippet will find the first headline with a level
+of 1 and a \"phone\" tag, and will return its beginning position:
+
+  \(org-element-map
+   tree 'headline
+   \(lambda (hl)
+     \(and (= (org-element-property :level hl) 1)
+          \(member \"phone\" (org-element-property :tags hl))
+          \(org-element-property :begin hl)))
+   nil t)
+
+Eventually, this last example will return a flat list of all
+`bold' type objects containing a `latex-snippet' type object:
+
+  \(org-element-map
+   tree 'bold
+   \(lambda (b)
+     \(and (org-element-map b 'latex-snippet 'identity nil t)
+          b)))"
   ;; Ensure TYPES and NO-RECURSION are a list, even of one element.
   (unless (listp types) (setq types (list types)))
   (unless (listp no-recursion) (setq no-recursion (list no-recursion)))
@@ -4168,8 +4224,8 @@ of the element and PROPS a plist of properties associated to the
 element.
 
 Possible types are defined in `org-element-all-elements'.
-Properties depend on element or object type, but always
-include :begin, :end, :parent and :post-blank properties.
+Properties depend on element or object type, but always include
+`:begin', `:end', `:parent' and `:post-blank' properties.
 
 As a special case, if point is at the very beginning of a list or
 sub-list, returned element will be that list instead of the first
@@ -4268,8 +4324,8 @@ associated to it.
 
 Possible types are defined in `org-element-all-elements' and
 `org-element-all-objects'.  Properties depend on element or
-object type, but always include :begin, :end, :parent
-and :post-blank properties."
+object type, but always include `:begin', `:end', `:parent' and
+`:post-blank'."
   (org-with-wide-buffer
    (let* ((origin (point))
 	  (element (org-element-at-point))