In SQL, consider the next example:
-- The table holding the result
CREATE TABLE #myTable(stringDate CHAR(7), dateValue DATETIME, newStringDate VARCHAR(20))
-- The values in original format
INSERT INTO #myTable(stringDate) SELECT '2014-01'
INSERT INTO #myTable(stringDate) SELECT '2014-02'
INSERT INTO #myTable(stringDate) SELECT '2014-03'
INSERT INTO #myTable(stringDate) SELECT '2015-01'
INSERT INTO #myTable(stringDate) SELECT '2015-02'
GO
-- All months have a first day, so conveting "2014-01" to date is just removing "-" and adding "01"
UPDATE #myTable SET dateValue = CAST(REPLACE(stringDate, '-', '') + '01' AS DATETIME)
GO
-- When we have the dates, you can tranform it to the format you want
UPDATE #myTable SET newStringDate = DATENAME(MONTH, dateValue) + ', ' + CAST(YEAR(dateValue) AS VARCHAR)
GO
SELECT * FROM #myTable